The Three Consumer's Surpluses

Recent years have seen a revival of interest in the concept of consumer's surplus. Among the new ideas and methods that have emerged, the use of the expenditure function is particuarly important. Diamond and McFadden (1974) show how it simplifies the discussion of Hicksian notions of the surplus based on compensated demand functions, viz. the compensating and equivalent variations. Seade (1976) and Willig (1976) show that in certain special cases, a simple function relation exists between these compensated surpluses and the conventional 'Marshallian' surplus defined using uncompensated or market demand functions. Willig introduces the ingenious idea of forgetting about the problem of the path-dependence of the Marshallian surplus by making it a convention to choose a particular path by a specified rule, and examines how well this surplus can approximate ont of the Hicksian surpluses. The purpose of this paper is complementary ; we show that the very conditions which make Marshallian surplus path - independent go a long way towards yielding bounds for it in terms of the Hicksian surpluses.